skip to main content

Title: Various notions of positivity for bi-linear maps and applications to tri-partite entanglement

We consider bi-linear analogues of s-positivity for linear maps. The dual objects of these notions can be described in terms of Schmidt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite versions of Schmidt numbers cover various kinds of bi-separability, and so we may interpret witnesses for those in terms of bi-linear maps. We give concrete examples of witnesses for various kinds of three qubit entanglement.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, The University of Suwon, Gyeonggi-do 445-743 (Korea, Republic of)
  2. Department of Mathematics and Institute of Mathematics, Seoul National University, Seoul 151-742 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22479612
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MAPS; QUANTUM ENTANGLEMENT; QUANTUM STATES; TENSORS